In signal processing, reconstruction usually means the determination of an original continuous signal from a sequence of measurements. For example, image reconstruction develops tools for numerically reconstructing images of a scene from measurements of the scene. The number of physical measurements provided by an imaging instrument is often limited due the hardware constraints. The image reconstruction considers the case when the total number of measurements falls below the number of pixels/voxels in the image. This makes image reconstruction an underdetermined problem with fewer measurements than unknowns. Hence, the image reconstruction is an ill-posed inverse problem. Several methods, such as iterative reconstruction and filtered back projection, have been developed to undress this problem.
Iterative reconstruction refers to iterative methods used to reconstruct 2D and 3D images in certain imaging techniques. The iterative reconstruction techniques are usually a better, but computationally more expensive alternative to the common filtered back projection, which directly calculates the image in a single reconstruction step. Modern fast computations and massive parallelism makes the iterative reconstruction more practical, but still challenging to deploy due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyper parameter selection.
Accordingly, there is a need for a neural network for performing reconstruction of a signal, for example, an image of a scene, from measurements of the scene.